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ISEE Lower Level Math : Geometry

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Example Questions

Example Question #22 : How To Find The Area Of A Triangle

What is the area of a equilateral triangle with a side length of and a height of ?

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

An equilateral triangle has three equal length sides so all the sides must be .

The area of a triangle is

$area= \frac{1}{2}*base*height$ .

The base is and the height is so,

$\\area=\frac{1}{2}*6*5 \\ \\area=\frac{1}{2}*30 \\ \\ area=15$

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Example Question #23 : How To Find The Area Of A Triangle

Find the area of a triangle with a base of 6cm and a height of 7cm.

Possible Answers:

$13\text{cm}^2$

$21\text{cm}^2$

$13\text{cm}$

$21\text{cm}$

$20\text{cm}^2$

Correct answer:

$21\text{cm}^2$

Explanation:

To find the area of a triangle, we will use the following formula:

$\text{area of triangle} = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

So, we know the base is 6cm and the height is 7cm. Knowing this, we can substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 6\text{cm} \cdot 7\text{cm}$

$\text{area of triangle} = \frac{1}{2} \cdot 42\text{cm}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{42\text{cm}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 42\text{cm}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{42\text{cm}^2}{2}$

$\text{area of triangle} = 21\text{cm}^2$

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Example Question #1251 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Find the area of a triangle with a base of 3in and a height that is two times the base.

Possible Answers:

$9\text{in}$

$9\text{in}^2$

$12\text{in}^2$

$18\text{in}^2$

$18\text{in}$

Correct answer:

$9\text{in}^2$

Explanation:

To find the area of a triangle, we will use the following formula:

$\text{area of triangle} = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle

Now, we know the base of the triangle is 3in. We also know the height of the triangle is two times the base. Therefore, the height is 6in. Knowing this, we can substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 3\text{in} \cdot 6\text{in}$

$\text{area of triangle} = \frac{1}{2} \cdot 18\text{in}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{18\text{in}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 18\text{in}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{18\text{in}^2}{2}$

$\text{area of triangle} = 9\text{in}^2$

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Example Question #322 : Geometry

Use the following triangle to answer the question:

Triangle1

Find the area of the triangle if it has a height of 8 inches.

Possible Answers:

$17\text{in}^2$

$12\text{in}^2$

$30\text{in}^2$

$18\text{in}^2$

$24\text{in}^2$

Correct answer:

$12\text{in}^2$

Explanation:

To find the area of a triangle, we use the following formula:

$\text{area of triangle} = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

Now, let's look at the triangle

Triangle1

We can see the base is 3in. We also know it has a height of 8in.

Knowing this, we can substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 3\text{in} \cdot 8\text{in}$

$\text{area of triangle} = \frac{1}{2} \cdot 24\text{in}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{24\text{in}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 24\text{in}^2}{2 \cdot1}$

$\text{area of triangle} = \frac{24\text{in}^2}{2}$

$\text{area of triangle} = 12\text{in}^2$

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Example Question #24 : How To Find The Area Of A Triangle

Use the following triangle to answer the question:

Triangle5

If the triangle has a height of 9ft, find the area.

Possible Answers:

$32\text{ft}^2$

$63\text{ft}^2$

$28\text{ft}^2$

$36\text{ft}^2$

$18\text{ft}^2$

Correct answer:

$18\text{ft}^2$

Explanation:

To find the area of a triangle, we will use the following formula:

$\text{area of triangle} = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

Now, given the triangle

Triangle5

we can see the base is 4ft. We also know it has a height of 9ft.

Knowing this, we can substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 4\text{ft} \cdot 9\text{ft}$

$\text{area of triangle} = \frac{1}{2} \cdot 36\text{ft}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{36\text{ft}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 36\text{ft}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{36\text{ft}^2}{2}$

$\text{area of triangle} = 18\text{ft}^2$

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Example Question #321 : Geometry

Find the area of a triangle with a base of 9in and a height of 12in.

Possible Answers:

$21\text{in}^2$

$27\text{in}^2$

$108\text{in}^2$

$33\text{in}^2$

$54\text{in}^2$

Correct answer:

$54\text{in}^2$

Explanation:

To find the area of a triangle, we will use the following formula:

$\text{area of triangle} = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

Now, we know the base of the triangle is 9in. We also know the height of the triangle is 12in.

Knowing this, we can substitute into the formula We get

$\text{area of triangle} = \frac{1}{2} \cdot 9\text{in} \cdot 12\text{in}$

Now, we can simplify things before we multiply to make things easier. The 2 in the denominator of the fraction and the 12 can both be divided by 2. So, we get

$\text{area of triangle} = \frac{1}{1} \cdot 9\text{in} \cdot 6\text{in}$

$\text{area of triangle} = 9\text{in} \cdot 6\text{in}$

$\text{area of triangle} = 54\text{in}^2$

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Example Question #31 : How To Find The Area Of A Triangle

Find the area of a triangle with a base of 4ft and a height that is two times the base.

Possible Answers:

$16\text{ft}^2$

$4\text{ft}^2$

$32\text{ft}^2$

$8\text{ft}^2$

$24\text{ft}^2$

Correct answer:

$16\text{ft}^2$

Explanation:

To find the area of a triangle, we will use the following formula:

$\text{area of triangle} = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

Now, we know the base of the triangle is is 4ft. We also know the height of the triangle is two times the base. Therefore, the height is 8ft.

Knowing this, we can substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 4\text{ft} \cdot 8\text{ft}$

$\text{area of triangle} = 2\text{ft} \cdot 8\text{ft}$

$\text{area of triangle} = 16\text{ft}^2$

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Example Question #33 : Triangles

Use the following triangle to answer the question.

Triangle7

If the triangle has a height of 7cm, find the area.

Possible Answers:

$32\text{cm}^2$

$24\text{cm}^2$

$16\text{cm}^2$

$28\text{cm}^2$

$14\text{cm}^2$

Correct answer:

$14\text{cm}^2$

Explanation:

To find the area of a rectangle, we will use the following formula:

$\text{area of triangle} = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

Now, given the triangle

Triangle7

We can see the base is 4cm. We also know the height is 7cm.

Knowing this, we can substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 4\text{cm} \cdot 7\text{cm}$

$\text{area of triangle} = 2\text{cm} \cdot 7\text{cm}$

$\text{area of triangle} = 14\text{cm}^2$

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Example Question #31 : How To Find The Area Of A Triangle

Find the area of a triangle with a base of 9cm and a height of 8cm.

Possible Answers:

$36\text{cm}$

$36\text{cm}^2$

$72\text{cm}$

$72\text{cm}^2$

$17\text{cm}^2$

Correct answer:

$36\text{cm}^2$

Explanation:

To find the area of a triangle, we will use the following formula:

$\text{area of triangle} = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

Now, we know the base is 9cm and the height is 8cm.

Knowing this, we can substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 9\text{cm} \cdot 8\text{cm}$

$\text{area of triangle} = 9\text{cm} \cdot 4\text{cm}$

$\text{area of triangle} = 36\text{cm}^2$

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Example Question #32 : How To Find The Area Of A Triangle

The base of a triangle is inches, and the height of the triangle is 3.5 inches. What is the area of the triangle?

Possible Answers:

10.25 $\textup{in.}^2$

24.25 $\textup{in.}^2$

24.5 $\textup{in.}^2$

12.25 $\textup{in.}^2$

12.20 $\textup{in.}^2$

Correct answer:

12.25 $\textup{in.}^2$

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two. The best answer is:

7 * 3.5 = 24.5

24.5/2 = 12.25

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ISEE Lower Level Math : Geometry

Study concepts, example questions & explanations for ISEE Lower Level Math

All ISEE Lower Level Math Resources

Example Questions

Example Question #22 : How To Find The Area Of A Triangle

Example Question #23 : How To Find The Area Of A Triangle

Example Question #1251 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Example Question #322 : Geometry

Example Question #24 : How To Find The Area Of A Triangle

Example Question #321 : Geometry

Example Question #31 : How To Find The Area Of A Triangle

Example Question #33 : Triangles

Example Question #31 : How To Find The Area Of A Triangle

Example Question #32 : How To Find The Area Of A Triangle

All ISEE Lower Level Math Resources

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